I love the word "pit". It has a primordial ring to it, images of a subterranean chamber of initiation come to mind, where transformation takes place. And that's what happens when paired with the word "barbecue".
Meat that is seasoned is lowered into a subterranean chamber or hole, or, into an above ground structure where the meat is cooked for many hours and is transformed into tender, flavorful, deliciousness. Whether subterranean, or above ground, shovels are often involved.
Certainly a tandoor is a pit, as is an Armenian tonir; a makeshift cinder block or more permanent brick pit also fits the category, as does a drum smoker. In 2007 the Culinary Historians of Southern California recreated an Early California pit barbecue at the Ygnacio Palomares Adobe in Pomona. It required burning hundreds of pounds of oak in the pit over the preceding night, then lowering cloth-wrapped, marinated beef shoulder clod into the resulting pit of coals and covering everything with earth. After cooking all night, participants pronounced the results "incredibly tender, deeply smoky meat."
I was fortunate to have experienced this myself in the hills of southern Orange County when I was around 12 years of age. Rich, smoky pull apart beef was served with tortillas, frijoles charros, and fresh salsa. It was exquisite, an experience I shall not forget, and hope to duplicate one day.